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We use the first systematic samples of CO millimeter emission in z>1'main-sequence' star forming galaxies (SFGs) to study the metallicitydependence of the conversion factor {\alpha}CO, from CO line luminosity tomolecular gas mass. The molecular gas depletion rate inferred from the ratio ofthe star formation rate (SFR) to CO luminosity, is ~1 Gyr-1 for near-solarmetallicity galaxies with stellar masses above M_S~1e11 M_sun. In this regimethe depletion rate does not vary more than a factor of two to three as afunction of molecular gas surface density, or redshift between z~0 and 2. BelowM_S the depletion rate increases rapidly with decreasing metallicity. We arguethat this trend is not caused by starburst events, by changes in the physicalparameters of the molecular clouds, or by the impact of the fundamentalmetallicity-SFR-stellar mass relation. A more probable explanation is that theconversion factor is metallicity dependent and that star formation can occur in'CO-dark' gas. The trend is also expected theoretically from the effect ofenhanced photodissociation of CO by ultraviolet radiation at low metallicity.From the available z~0 and z~1-3 samples we constrain the slope of thelog({\alpha}CO) -log (metallicity) relation to range between -1 and -2, fairlyinsensitive to the assumed slope of the gas-star formation rate relation.Because of the lower metallicities near the peak of the galaxy formationactivity at z~1-2 compared to z~0, we suggest that molecular gas massesestimated from CO luminosities have to be substantially corrected upward forgalaxies below M_S.

The metallicity dependence of the CO {\rightarrow} H_2 conversion factor in z>1 star forming galaxies